Finite Group Databasebeta

← #11887579

Subgroups — #11887579

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594515C211yesmaximal, characteristic
2#10594383C211yesmaximal, characteristic, complemented
3#10592561C211yesmaximal, characteristic, complemented
4C3×#4862C211yesmaximal, characteristic, complemented
5C3×#4852C211yesmaximal, characteristic, complemented
6#10590890C211yesmaximal, characteristic, complemented
7#10590824C211yesmaximal, characteristic, complemented
8#10590822C211yesmaximal, characteristic, complemented
9#10590721C211yesmaximal, characteristic, complemented
10#10590601C211yesmaximal, characteristic, complemented
11D3×#810C211yesmaximal, characteristic, complemented
12#10590559C211yesmaximal, characteristic, complemented
13#10590556C211yesmaximal, characteristic, complemented
14#10590507C211yesmaximal, characteristic, complemented
15#10590501C211yesmaximal, characteristic, complemented
16#81450—31nomaximal
17#79678—31nomaximal
18C2×#3798—21no—
19C2×#3797C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21#64106C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C2×C3×#204C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63918—21no—
29#63918C2211yescharacteristic
30#63916C2211yescharacteristic
31#63908C2211yescharacteristic
32#63905—21no—
33C4×#626C2211yescharacteristic
34#63895—21no—
35#63893—21no—
36#63880—21no—
37#63866C2211yescharacteristic
38#63853—21no—
39#63851—21no—
40C2×#3716C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3710C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#106C2211yescharacteristic
45#63647C2211yescharacteristic
46#63643C2211yescharacteristic
47#63637C2211yescharacteristic
48#63635C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#809C2211yescharacteristic
55C3×#808C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63566C2211yescharacteristic
60#63565C2211yescharacteristic
61#5632—31no—
62Q8×D12—31no—
63#5551—31no—
64#5507—31no—
65C3×#483—31no—
66C3×C4×SD16—31no—
67#5170—31no—
68#5170—31no—
69#5048—31no—
70#5020—31no—
71#5019—31no—
72C2×#810—31no—
73#4864—31no—
74#4862—31no—
75#4862—31no—
76#4862—61no—
77#4862D311yescharacteristic, complemented
78#4854—31no—
79#4852D311yescharacteristic, complemented
80#4818—31no—
81#4806—31no—
82D3×#103—31no—
83D3×#103—31no—
84D3×#103—31no—
85#4792—31no—
86#4778—31no—
87#4778—31no—
88#4738—31no—
89#67⋊C8—31no—
90C8×D12—31no—
91#4681—31no—
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#627—21no—
102C2×#627—21no—
103C2×#627—21no—
104C2×#626—21no—
105C2×#626D411yescharacteristic
106C2×#625—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109#3798—44no—
110#3797—22no—
111#3797—41no—
112D3×Dic6—22no—
113D3×Dic6—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117#3752—21no—
118C4⋊(C3⋊Dic3)—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×#204—22no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141#3716—41no—
142#3715—41no—
143#3710—41no—
144D3×C3⋊C8—41no—
145#3298—91noSylow
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8—31no—
149C2×#235—61no—
150C2×#235—61no—
151C22×Dic6—31no—
152C2×C3×SD16—31no—
153C3×C22⋊Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—31no—
156C2×C3×C4⋊C4—31no—
157#944—31no—
158C2×#215—31no—
159#938—31no—
160#938—31no—
161C2×#214—31no—
162C2×#214—31no—
163#930—31no—
164#929—61no—
165C4×#67—31no—
166#924—61no—
167C22×C3⋊C8—31no—
168C2×#204—31no—
169C2×#204C2×D311yescharacteristic
170C2×D3×C8—31no—
171C2×D3×C8—31no—
172C2×D3×C8—31no—
173#897—31no—
174#897—31no—
175#897—61no—
176#897—61no—
177#897—61no—
178#897C2×D311yescharacteristic
179#896—61no—
180#896—61no—
181#895—31no—
182#894—61no—
183#893C2×D311yescharacteristic
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—61no—
187D3×C4⋊C4C2×D311yescharacteristic
188#888—31no—
189#888—61no—
190#887C2×D311yescharacteristic
191#883—61no—
192#883—61no—
193#67⋊C4—61no—
194#878—61no—
195C4×D12—31no—
196C4×D12—61no—
197#869—31no—
198#869—31no—
199#869—61no—
200C3×#106—21no—
201C3×#106—31no—
202C3×#106C2×D311yescharacteristic
203C3×#106C2×D311yescharacteristic
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#102—31no—
208C3×C22⋊C8—31no—
209C3×C4×C8—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—61no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217#816—31no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—61no—
223#816C2×D311yescharacteristic
224Dic3⋊C8—31no—
225C8×Dic3C2×D311yescharacteristic
226#810—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—61no—
231#810C2×D311yescharacteristic
232#810C2×D311yescharacteristic
233#809C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—61no—
237#808C2×D311yescharacteristic
238C4⋊(C3⋊C8)—31no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4×C3⋊D3—21no—
249C4×C3⋊D3—21no—
250C4×C3⋊D3—42no—
251#634—21no—
252#634—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—42no—
264C3×C4×D3—42no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6#4112yescomplemented
269#627—42no—
270#627—42no—
271#627—42no—
272#626—42no—
273#626SD1614yescomplemented
274#625—42no—
275#624—42no—
276D3×Dic3—42no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281D4×Q8—91no—
282#547—91no—
283#487—91no—
284#483—31no—
285#483—91no—
286#475—91no—
287#465—91no—
288#465—91no—
289#461—91no—
290#448—91no—
291#448—91no—
292C4×SD16—31no—
293C8×D4—91no—
294C2×#103—91no—
295C2×#103—91no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×D4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C2×#67—31no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C22×Dic3—61no—
307D3×Q8—62no—
308D3×Q8—62no—
309D3×Q8—62no—
310D3×Q8—121no—
311D3×Q8—121no—
312D3×Q8—121no—
313#235—124no—
314#235—124no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12C22×D311yescharacteristic
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—121no—
329C2×C4×D3C22×D311yescharacteristic
330C2×Dic6—31no—
331C2×Dic6—31no—
332C2×Dic6—61no—
333C2×Dic6—62no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—121no—
341C2×Dic6C22×D311yescharacteristic
342C2×Dic6C22×D311yescharacteristic
343C3×SD16—62no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—31no—
362C3×C42—61no—
363#217—31no—
364#217—61no—
365#217—61no—
366#215—121no—
367#214—121no—
368#214—121no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—121no—
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—121no—
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—31no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—121no—
400C4×Dic3—21no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408#204—22no—
409#204—121no—
410D3×C8—121no—
411D3×C8—121no—
412D3×C8—121no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3C2×SD1612yes—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3C2×SD1612yes—
423C32×C4—41no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—22no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3C2×SD1612yes—
436C2×#41—181no—
437C22×Q8—91no—
438C22×Q8—91no—
439C2×SD16—31no—
440C2×SD16—91no—
441C2×SD16—91no—
442C22×C8—91no—
443C22×C8—91no—
444C4⋊Q8—91no—
445C4⋊Q8—91no—
446C4⋊Q8—181no—
447#123—181no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451C22⋊Q8—181no—
452C22⋊Q8—181no—
453C22⋊Q8—181no—
454#121—91no—
455#121—91no—
456C4×Q8—31no—
457C4×D4—31no—
458C4×D4—91no—
459C4×D4—181no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—91no—
462#106—31no—
463#106—91no—
464#106D3211yescharacteristic
465C4⋊C8—91no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#102—31no—
476C22⋊C8—31no—
477C22⋊C8—91no—
478C4×C8—31no—
479C23×C3—31no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—31no—
483C22×D3—31no—
484C22×D3—61no—
485C22×D3D3×D411yescharacteristic
486C3×Q8—32no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×D4—61no—
491C3×D4—61no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—122no—
508C2×C3×C4—122no—
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—34no—
512#67—122no—
513#67—122no—
514#67—122no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—121no—
526C2×Dic3—121no—
527C2×Dic3—122no—
528C2×Dic3D3×D411yescharacteristic
529C2×Dic3D3×D411yescharacteristic
530C2×Dic3D3×D411yescharacteristic
531D12—21no—
532D12—21no—
533D12—34no—
534D12—122no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—42no—
538C4×D3—42no—
539C4×D3—61no—
540C4×D3—61no—
541C4×D3—61no—
542C4×D3—61no—
543C4×D3—121no—
544C4×D3—121no—
545C4×D3—122no—
546C4×D3—122no—
547C4×D3—122no—
548C4×D3—122no—
549C4×D3—122no—
550C4×D3—242no—
551Dic6—21no—
552Dic6—21no—
553Dic6—21no—
554Dic6—61no—
555Dic6—61no—
556Dic6—61no—
557Dic6—61no—
558Dic6—121no—
559Dic6—121no—
560Dic6—122no—
561Dic6—122no—
562Dic6—122no—
563Dic6—122no—
564Dic6—122no—
565Dic6—122no—
566Dic6#23512yescomplemented
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—41no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C2×C32#54611yescharacteristic
578C2×C32C22×SD1611yescharacteristic
579C2×C32#57811yescharacteristic
580C3⋊D3—22no—
581C3×D3—22no—
582C3×D3—81no—
583#41—364no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×Q8—91no—
587C2×Q8—181no—
588C2×Q8—181no—
589C2×Q8—181no—
590C2×Q8—182no—
591C2×Q8—182no—
592C2×Q8—361no—
593C2×Q8—361no—
594C2×D4—31no—
595C2×D4—91no—
596C2×D4—181no—
597C2×D4—181no—
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—91no—
602C22×C4—181no—
603C22×C4—181no—
604C22×C4—181no—
605SD16—62no—
606SD16—361no—
607SD16—361no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—91no—
611C2×C8—361no—
612C2×C8—361no—
613C2×C8C2×D3211yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4C2×D3211yescharacteristic
626C4⋊C4C2×D3211yescharacteristic
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—91no—
630C22⋊C4—91no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—31no—
635C42—61no—
636C22×C3—21no—
637C22×C3—32no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3C2×D3×D411yescharacteristic
644C22×C3C2×D3×D411yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—32no—
648C2×D3—32no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—62no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3D3×SD1612yes—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—32no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—62no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—81no—
671C3×C4—81no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4C2×#23511yescharacteristic
675C3×C4D3×#4111yescharacteristic
676C3×C4#100911yescharacteristic
677C3×C4#100911yescharacteristic
678Dic3—21no—
679Dic3—21no—
680Dic3—22no—
681Dic3—41no—
682Dic3—41no—
683Dic3—61no—
684Dic3—61no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—241no—
691Dic3—241no—
692Dic3D3×SD1612yes—
693C32#329811yescharacteristic, complemented, Sylow
694C23—31no—
695C23—61no—
696C23—91no—
697Q8—32no—
698Q8—61no—
699Q8—61no—
700Q8—61no—
701Q8—181no—
702Q8—181no—
703Q8—362no—
704Q8—362no—
705Q8—362no—
706D4—61no—
707D4—61no—
708D4—94no—
709D4—362no—
710D4—362no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—91no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—181no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—362no—
729C2×C4—362no—
730C2×C4—362no—
731C2×C4C22×D3211yescharacteristic
732C8—21no—
733C8—61no—
734C8—61no—
735C8—181no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—62no—
740C2×C3—241no—
741C2×C3#555011yescharacteristic
742C2×C3#565411yescharacteristic
743C2×C3C2×D3×SD1611yescharacteristic
744C2×C3C2×D3×SD1611yescharacteristic
745C2×C3#577111yescharacteristic
746C2×C3#577911yescharacteristic
747D3—22no—
748D3—62no—
749D3—62no—
750D3—81no—
751D3—122no—
752C22—32no—
753C22—61no—
754C22—61no—
755C22—92no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22—181no—
760C22—181no—
761C22D32×D411yescharacteristic
762C4—32no—
763C4—41no—
764C4—41no—
765C4—61no—
766C4—62no—
767C4—61no—
768C4—121no—
769C4—121no—
770C4—181no—
771C4—361no—
772C4—361no—
773C4D3×#23511yescharacteristic
774C4#6432011yescharacteristic
775C3—21no—
776C3#7967811yescharacteristic, complemented
777C3#8145011yescharacteristic, complemented
778C2—62no—
779C2—182no—
780C2—241no—
781C2#1059461911yescharacteristic
782C2D32×SD1611yescharacteristic
783C2#1059475611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10594515C2
hypercenter#106D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10594383C2semidirect
3. #10592561C2semidirect
4. C3×#4862C2semidirect
5. C3×#4852C2semidirect
6. #10590890C2semidirect
7. #10590824C2semidirect
8. #10590822C2semidirect
9. #10590721C2semidirect
10. #10590601C2semidirect
11. D3×#810C2semidirect
12. #10590559C2semidirect
13. #10590556C2semidirect
14. #10590507C2semidirect
15. #10590501C2semidirect
77. #4862D3semidirect
79. #4852D3semidirect
268. C3×Dic6#41semidirect
273. #626SD16semidirect
566. Dic6#235semidirect
693. C32#3298semidirect
776. C3#79678semidirect
777. C3#81450semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105945152
#105943832
#105925612
C3×#48622
C3×#48522
#105908902
#105908242
#105908222
#105907212
#105906012
D3×#8102
#105905592
#105905562
#105905072
#105905012
#814503
#796783